1. The H 2 + Molecule One electron problem Two nuclei Define electron position, ie. internal coordinates, w.r.t. nuclear positions.

2. The H 2 + Molecule Since Z A =1 and Z B =1

3. The H 2 + Molecule Nuclear Electronic The nuclear positions determine the electronic wavefunction Assume electronic motion is much faster than nuclear motion, implies that the nuclear positions are essentially static The electronic part is determined by the nuclear positions Separable?? W- Total Energy

4. The H 2 + Molecule Potential energy surface. Of primary interest Nuclear Electronic

5. Linear Variational WFctns. Suppose the trial wavefunction can be expressed in terms of an expansion of an appropriate set of functions, not necessarily othonormal

6. Linear Variational WFctns. For each c i Find the optimum coefficients, that minimize E var. 1 1

7. Linear Variational WFctns. Need to diagonalize matrix, to find eigenvalues and eigen vectors:

8. Linear Combination of Atomic Orbitals. Lets use the 1s Hydrogen like orbitals to be a basis for a trial function and apply variational theory to find the best approximate wavefunction Whereare Hydrogen like wavefunction with n=1, l=0, centred in nucleus a and b, resp.

9. Linear Combination of Atomic Orbitals.

12. Prediction of the Bond

13. Bonding and Antibonding Orbitals of H 2 +

14. 23_09fig_PChem.jpg Density Difference Between MO’s and 1s O’s

15. 23_11fig_PChem.jpg Electron Densities of Sigma and Pi M.O’.s Bonding Antibonding g=gerade (same) u=ungerade (opposite)

16. -13.6 e.v. -19.6 e.v. -18.6 e.v. Electron population on F is larger, ie. bond in polarized to F, ie. shows the F is more electronegative. Other Types of M.O.’s

17. 23_13fig_PChem.jpg MO’s for the Diatomics

18. 23_02tbl_PChem.jpg Energy Level Diagram For the Diatomics Electron Configuration for H 2 &He 2

19. 23_17fig_PChem.jpg Electron Configuration of N 2

20. 23_16fig_PChem.jpg Electron Configuration of F 2

21. 23_18fig_PChem.jpg Electron Configurations of the Diatomics

22. 23_20fig_PChem.jpg Bonding in HF